[nkhodyunya]

I think early math education suffers from the lack of awareness about how important is exactness in math. People come to math from real world, where they don't mind to be rigorous about the meaning of every word. Most newcomers tend to skip words they don't find interesting and then penalty seems to come from nowhere. And education even encourages such error-prone behaviour, by giving wrong exercises and poor material.

Math isn't hard, it just doesn't work for those who don't know how to use it. And knowing how to use it means understanding what exactly you are doing. Many students don't bother about what does it mean to do when asked to solve an equation.

[dboreham]

This resonates very strongly with my experience helping my two kids (11,13) with their math work. Their teachers have not always been as helpful as they might in this respect, for example marking test solutions as entirely incorrect when the student has made a stupid arithmetic mistake in the working but otherwise demonstrated a proper understanding of how to solve the problem. I'm not arguing that incorrect answers should be rewarded, but it does seem to demotivate the student when they are punished for a mistake performing a task that no adult would need to perform (we use computers and calculators for our arithmetic, and have done since I was my kids age in the 1970s).